Recursive estimation of the mode of a multivariate density

Let f be an unknown possibly multimodal density on Rd and let X1, X2, … be a sequence of independent random vectors with density f. Several recursive estimates of the mode of f are proposed, and sufficient conditions ensuring their weak and strong consistency are established. Soit f une densite inconnue possiblement multimodale definie dans Rd et soit X1,x2,…un echantillon aleatoire ayant une densite egale a f, On propose plusienurs estimateurs recursifs du mode de f, et on presente des conditions souc lesquelles ces estimateurs sont faiblement ou fortement consistents.

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